# To classify: The function y = π x as one of the type of functions.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.2, Problem 2E

(a)

To determine

## To classify: The function y=πx as one of the type of functions.

Expert Solution

The function y=πx is an exponential function.

### Explanation of Solution

Reason:

An exponential function is of the form f(x)=bx , where b is a positive constant and x is an exponent. Here, b=π . Thus, the given function is said to be an exponential function.

(b)

To determine

### To classify: The function y=xπ as one of the type of functions.

Expert Solution

The function y=xπ is a power function.

### Explanation of Solution

Reason:

The power function y=xπ is of the form f(x)=xn , where n is a positive integer. Here, the variable x is called as base. Thus, the given function is said to be a power function.

(c)

To determine

### To classify: The function y=x2(2−x3) as one of the type of functions.

Expert Solution

The function y=x2(2x3) is a polynomial function.

### Explanation of Solution

Reason:

Rewrite the given function as y=2x2x5 .

The polynomial function is of the form p(x)=anxn+an1xn1+...+a1x+a0 , where n is a positive integer and a0,a1,...,an are constants. Thus, the given function is a polynomial function with degree 5.

(d)

To determine

### To classify: The function y=tant−cost as one of the type of functions.

Expert Solution

The function y=tantcost is a trigonometric function.

### Explanation of Solution

Reason:

The function involves with the trigonometric functions such as cost and tant . Thus, the given function is said to be a trigonometric function.

(e)

To determine

### To classify: The function y=s1+s as one of the type of functions.

Expert Solution

The function y=s1+s is a rational function.

### Explanation of Solution

Reason:

The function is of the form f(s)=p(s)q(s) , where p(s) and q(s) are the polynomials and q(s)0 is said to be a rational function. Here, p(s)=s and q(s)=1+s . Thus, the given function is a rational function.

(f)

To determine

### To classify: The function y=x3−11+x3 as one of the type of functions.

Expert Solution

The function y=x311+x3 is an algebraic function.

### Explanation of Solution

Reason:

The function y=x311+x3 involves with polynomial and root functions. Thus, the given function is an algebraic function.

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